We recall the notion of relative degree for system (REF ), see e.g. [1]}.
Assuming that \(f,g,h\)  are sufficiently smooth, the Lie derivative of \(h\)  along \(f\)  is defined by \(\left(L_f h\right)(x) = h^{\prime }(x) f(x)\) , and successively we define \(L_f^k h = L_f (L_{f}^{k-1} h)\)  with \(L_f^0 h = h\) .
Furthermore, for the matrix-valued function \(g\)  we have
\((L_gh)(x) = \left[(L_{g_1}h)(x), \ldots , (L_{g_m}h)(x) \right],\) 
